Vibration Analysis of Timoshenko Beam Subjected to a Moving Mass and Suffering from an Open Crack

Abstract

This study has considered free and forced vibration analysis of a cracked Timoshenko beam exposed to a moving mass. It considers both analytical and finite element (FE) methods to analyse the vibration response of a simply supported beam carrying a moving mass and suffering from an open crack. Timoshenko beam theory has deliberated to investigate the dynamic behavior of a discretely simply supported beam with including shear deformation and rotational inertia under various configurations of open crack and moving mass conditions. The beam was divided into two segments, which obeyed the Timoshenko beam theory and the crack was modeled by a torsional spring with local elasticity at the connecting region of the two segments. The governing equations of the beam transverse vibration were solved based on Hamilton’s principle, and the obtained results are validated with previously published works, including numerical and experimental works. The effect of crack depth (CD) and crack location (CL) with the amount and speed of the moving mass on the dynamic response of the beam have been investigated, where the presence of the crack plays a key role in both free vibration characteristics and dynamic response of the Timoshenko beam. Hence, more nonlinearity and higher deflection in the dynamic behavior have perceived at CL = 0.5 and CD > 0.3 h. The obtained natural frequencies are generally decreased with increasing CD, in which significant drop in the 1st and 3rd natural frequencies have been identified when the crack is located at the mid-span of the beam. A frequency-domain representation under various mode excitations of moving load has evaluated to indicate the presence of the crack within the Timoshenko beam. Hence, the evaluation of frequency domain and dynamic deflection can be sensitive to indicate the presence of the crack and its severity.